Recently Active Calculus Questions

Let f(x) be a funcn. differentiable on [ 0 , a ] such that f(0) = 1 , f(a) = 31/6 . If f'(x) is greater than equal to [f(x)]4 + [f(x)]-2 , then the max. value of a is: (a) pi/6 (b) pi/12 (c) pi/24 (d) pi/36 ...

hello,im getting an old Arihant Integral Calculus of Amit M Agarwal for 70rs only :D should i buy it ,but its of 2002 edition! ...

Let f(x) = x2 − 2x. How many distinct real numbers "c" satisfy f(f(f(f(c)))) = 3? ...

Integrate {0 to π} [cotx ]dx , where [ . ] denotes the greatest integer function, is equal to? ...

if a continous function satisfies F(F(x))=1/F(x) and F(1000)=999, Find F(500) ...

F(x) = (x3 + 3x - 14)(x2 + 3x - 10) , has a local maxima at ?? ...

1. f(a-x) = f(a+x) and f(b-x) = f(b+x) for all Real x, where a and b are constants and a>b, then find the period. ?? My Ans: ?? I found 2(a-b), but a sir is saying it's not correct! ...

for a function f(x) satisying f(0)=1,f'(0)=-1,f(x)>0 for all x,what can we say regarding f''(x) ...

1. \lim_{x\rightarrow 0^{-}} \frac{\sum_{r =1}^{2n+1}{[x^{r}]+(n+1)}}{1+[x]+|x|+2x} 2. \lim_{x\rightarrow 0} \left\{\lim_{n\rightarrow \infty } \left(\frac{[1 (sinx)^{x}]+[2^{2}(sinx)^{x}] + .....}{n^{3}} \right) \right\} ...

limn→∞ limm→∞ cos2m(n!pix)x belongs to R prove the above function =1 if x is rational function =0if x is irrational ...

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f is a real valued infinitely differentiable function.f(0) = 0 and f"(x) >0 for all real x then f(x)/x is 1) increasing on (0,∞) 2) increasing on (-∞,∞) 3)decreasing on (0,∞) 3)decreasing on (-∞,∞) ...

Find all solution of f(f(x))=x ...

\mathbf{\int sin(101x)sin^{99}xdx}= ...

1) Evaluate the limit: \lim_{n\to\infty} |\sin (\pi\sqrt{n^2+n+1})| 2) Prove that \lim_{n\to \infty}n^2 \int_0^{1/n} x^{x+1}\ \mathrm dx=\dfrac{1}{2} 3) Find the real parameters m and n such that the graph of the function f(x ...

Let f:[0,2]→R be defined by f(x)=\sqrt{x^3+2-2\sqrt{x^3+1}}+\sqrt{x^3+10-6\sqrt{x^3+1}} Find the indefinite integral of f w.r.t x. ...

Given that \int_{-\infty}^{\infty} e^{-x^2}\ \mathrm dx=\sqrt{\pi} evaluate the integral I=\int_0^\infty \dfrac{1}{\sqrt{x}}\ e^{-x}\ \mathrm dx ...

1) Prove: \left|\begin{array}{cccc} 1+a_1 & 1 & \cdots & 1\\1 & 1+a_2 & \cdots & 1\\\vdots & \vdots & \ddots & \vdots \\1 & 1 & \cdots & 1+a_n\end{array}\right| = a_1a_2\cdots a_n \left(1+\dfrac{1}{a_1}+ \dfrac{1}{a_2}+\ldots ...

*Image* whcih theorem to use for solving option c and d ...

Q1)lim (x+2)tan-1(x+2) - x tan-1x (x→ ∞) Q2) lim ((1.5)n+ [(1+0.0001)10000]n)1/n (x→ ∞) Here[ ] is Greatest Integer Function (GIF) n Q3) lim Σ log( 1 +K/n)1/n (n→∞) k=1 Thnx in advance ...

the area bounded by the curve {|x|, |y|}= 1/2 is ...

*Image* find answer ...

solve it and find answer *Image* ...

Let P(x) be the non constant polynomial of smallest degree such that (x − 4)P(x2 − 4) = xP(x − 2)P(x − 4). What is P(5)? ...

The area bounded by mod(2x+y) + mod(x-2y) ≤4 [where mod→modulus] ...

*Image* how to make this problem dance??...i mean how to solve it [3] ...

If f:[0,1]→[0,1] be a continuous function such that f(f(x))=1 for all x in[0,1]. Find all possible values of ∫f(x) dx with 0 to 1 as limits of integration ...

draw graph of {\color{green} y}{\color{blue} =}{\color{red} e^{e^{x}}} ...

If I(m,n)=\int_{0}^{1}{t^m(1+t)^ndt} , then the expression for I(m,n) in terms of I(m+1,n-1) is: a) 2n/m+1 - n/m+1 I(m+1,n-1) b) n/m+1 I(m+1,n-1) c) 2n/m+1 + n/m+1 I(m+1,n-1) d) m/n+1 I(m+1,n-1) DISCLAIMER:: Show Steps..! Els ...

Limit x->0+ x^(cosx ) ...